4Key Concepts1st level analysis – A within subjects analysis where activation is averaged across scans for an individual subjectThe Between- subject analysis is referred to as a 2nd level analysis and will be described later on in this courseDesign Matrix – 2D, m = regressors, n = time. A dark-light colour map is used to show the value of each variable at specific time pointsThe Design Matrix forms part of the General linear model, the majority of statistics at the analysis stage use the GLMRebecca Knight

5Y X β + E x = General Linear Model Generic ModelDependent Variable (What you are measuring)Independent Variable (What you are manipulating)Relative Contribution (These need to be estimated)Error (The difference between the observed data and that which is predicted by the model)Aim: To explain as much of the variance in Y by using X, and thus reducing EY = X1β1 + X2β X n βn EMore than 1 IV ?

6GLM ContinuedHow does this equation translate to the 1st level analysis ?Each letter is replaced by a set of matrices (2D representations)YXβ+Ex=Matrix of BOLD signals(What you collect)Design matrix(This is what is put into SPM)Matrix parameters(These need to be estimated)Error matrix(residual error for each voxel)TimeTimeTimeRegressorsVoxelsVoxelsRegressorsVoxels

9RegressorsRegressors – represent hypothesised contributors in your experiment. They are represented by columns in the design matrix (1column = 1 regressor)Regressors of Interest or Experimental Regressors – represent those variables which you intentionally manipulated. The type of variable used affects how it will be represented in the design matrixRegressors of no interest or nuisance regressors – represent those variables which you did not manipulate but you suspect may have an effect. By including nuisance regressors in your design matrix you decrease the amount of error.E.g. - The 6 movement regressors (rotations x3 & translations x3 ) or physiological factors e.g. heart rate

10RegressorsA dark-light colour map is used to show the value of each regressor within a specific time pointBlack = 0 and illustrates when the regressor is at its smallest valueWhite = 1 and illustrates when the regressor is at its largest valueGrey represents intermediate valuesThe representation of each regressor column depends upon the type of variable specifiedTime(n)Regressors (m)Rebecca Knight

11ConditionsAs they indicate conditions they are referred to as indicator variablesType of dummy code is used to identify the levels of each variableE.g. Two levels of one variable is on/off, represented asON = 1OFF = 0Changes in the bold activation associated with the presentation of a stimulusWhen you IV is presentedRed box plot of [0 1] doesn’t model the rise and fallsWhen you IV is absent (implicit baseline)Fitted Box-Car

12Modelling HaemodynamicsChanges in the bold activation associated with the presentation of a stimulusHaemodynamic response functionPeak of intensity after stimulus onset, followed by a return to baseline then an undershootBox-car model is combined with the HRF to create a convolved regressor which matches the rise and fall in BOLD signal (greyscale)Even with this, not always a perfect fit so can include temporal derivatives (shift the signal slightly) or dispersion derivatives (change width of the HRF response) *more later in this courseHRF Convolved

13Covariates What if you variable can’t be described using conditions?E.g Movement regressors – not simply just one state or anotherThe value can take any place along the X,Y,Z continuum for both rotations and translationsCovariates – Regressors that can take any of a continuous range of values (parametric)Thus the type of variable affects the design matrix – the type of design is also important

14Designs Block design v Event- related designIntentionally design events of interest into blocksRetrospectively look at when the events of interest occurred. Need to code the onset time for each regressor

15Separating RegressorsThe type of design and the type of variables used in your experiment will affect the construction of your design matrixAnother important consideration when designing your matrix is to make sure your regressors are separateIn other words, you should avoid correlations between regressors (collinear regressors) – because correlations in regressors means that variance explained by one regressor could be confused with another regressorThis is illustrated by an example using a 2 x 3 factorial design

17Example Cont.V A C1 C2 C3If you made each level of the variables a regressor you could get 5 columns and this would enable you to test main effectsBUT what about interactions? How can you test differences between Mh and NlThis design matrix is flawed – regressors are correlated and therefore a presence of overlapping variance (Grey)M N h m lM N h m lMN h ml

18Orthogonal design matrixM M M N N NIf you make each condition a regressor you create 6 columns and this would enable you to test main effectsAND it enable you to test interactions! You can test differences between Mh and NlThis design matrix is orthogonal – regressors are NOT correlated and therefore each regressor explains separate varianceh m l h m lM M M N N Nh m lh m l h m lMNhmlMNMhMmMlNhNmNl

19β Y X + E x = Summary Matrix of BOLD signals Design matrixMatrix parametersError matrixTimeTimeTimeRegressorsVoxelsVoxelsRegressorsVoxelsAim: To explain as much of the variance in Y by using X, and thus reducing Eβ = relative contribution that each regressor has, the larger the β value = the greater the contributionNext: Examine the effect of regressors

20Outline What are contrasts? Why do we need contrasts? T contrastsF contrastsRebecca Knight

21Why use contrasts GLM: - Specify design matrix- Determine β’s for each voxel for each regressorUse contrasts to:- Specify effects of interest- Perform statistical evaluation of hypothesesContrasts used and their interpretation depends on the modelspecification, which in turn depends on the design of theexperimentRebecca Knight

37InferenceWe’ve talked about 1st level so far… examining within subjectvariability.However, we can’t use a sample of one to extrapolate our findings tothe general population2nd level analyses to look for effects at the group level… discussedlater in courseRebecca Knight